U.S. Pat No. 4,163,324 discloses a method to determine the direction of a borehole during drilling using a triaxial accelerometer/magnetometer-package arranged in the drill string, the method including the steps of:
measuring gravity acceleration components g.sub.x, g.sub.y, g.sub.z of the known local gravity acceleration vector g for determining inclination angle .theta. and highside angle .phi., and PA1 measuring magnetic field components B.sub.x, B.sub.y, B.sub.z of the total magnetic field B for determining azimuth angle .psi.; x, y and z indicating vector components in a Cartesian XYZ-coordinate system fixed to the package during drilling, and .psi., .theta., and .phi. indicating angles defining rotations between said XYZ-system and a Cartesian NEV-coordinate system, with N the magnetic north direction, V the vertical g-direction, and E the east direction. PA1 measuring gravity acceleration components g.sub.x, g.sub.y, g.sub.z of the gravity acceleration vector gat a plurality of locations within the borehole where each location within the borehole is l.sub.i where i are consecutive positive integers; PA1 determining inclination angle .theta. and highside angle .phi. of the borehole at each of locations within the borehole based on the gravity acceleration components; PA1 measuring, at each of the locations within the borehole, magnetic field components B.sub.x, B.sub.y, B.sub.z of the total magnetic field B; and PA1 determining azimuth angle .psi. at each of the locations within the borehole wherein azimuth angles .psi. are calculated in accordance with EQU B.sub.i =[.phi..sub.i ].sup.T [.theta..sub.i ].sup.T {[.psi..sub.i ].sup.T B.sub.e }+B.sub.p
Patent '324 discloses a drill string comprising a drilling bit that is coupled at one side by a non-magnetic drill collar and at the other side by a set of drill collars made of magnetic material. The set is further coupled to a drill pipe. The non-magnetic collar contains a survey instrument, for example a triaxial accelerometer/magnetometer package. When measuring the total magnetic field B, additional to the earth's magnetic field B.sub.e a perturbating magnetic field B.sub.p is included, for example from the above said bit and/or set of drill collars. In the method of patent '324 it is assumed that the effect of the magnetic drill string can be approximated by only a B.sub.p -vector along the borehole axis Z, B.sub.p,z. This assumption enables calculation of an uncorrected azimuth angle, and in a next step to apply an iteration procedure to determine a first order correction. In many conditions, however, the assumption of only a B.sub.p,z and the approximation of B.sub.p,z are far from realistic.
For example it is well known that during drilling a non-magnetic collar may become magnetized resulting in so-called hot spots encompassing perturbating magnetic field vectors having unpredictable directions.
In U.S. Pat. No. 4,682,421 a method is presented for determining an azimuth angle that is corrected for drill string magnetization by calculating the perturbating erroneous magnetic field M at the location of the instrument. In particular a two-step approach of the above problem is disclosed. After determining the gravity acceleration vector g and measuring the total magnetic field B.sub.m (equal to B.sub.e +M), in a first step the cross-axial component M.sub.xy of M is determined. At least three x-y-measurements are necessary for the first step because M.sub.xy is derived graphically from a circle made up of these measurements. The measurements are carried out by rotating the drill string at one location along the borehole axis, being the Z-axis in the measurement coordinate system. It may be clear to those skilled in the art such rotation of the drill string at one location will delay the borehole drilling operation.
The second step of patent '421 involves a geometrical determination of M.sub.z. However, because the application of the cosine-rule (as shown in FIG. 3 of patent '421) for obtaining a minimum error value has to be restricted mathematically to a plane comprising all the relevant parameters including .theta. and 74 .sub.0, the determination as presented can only be considered an approximation. Possible errors in M.sub.z and .psi. are therefore dependent on errors in parameters already used in the cosine-rule.
Thus, it is an object of the present invention to overcome the problem of rotating the drill string each time the direction of the borehole has to be determined. It is a further object of the present invention to present a method enabling determination of azimuth angles which result from straight forward calculation. It is another object of the present invention to arrive at a method resulting in parameter values which are calculated independently thereby avoiding propagating error calculus.